Theoretical and Mathematical Physics

, Volume 157, Issue 2, pp 1514–1524 | Cite as

A nonlinear eigenvalue problem

Article

Abstract

We reduce the problem of the zeros of an entire function related to the Painlevé I equation to the eigenvalue problem for the Dirichlet problem for a fourth-order bilinear equation. In a simplified case, this problem reduces to the problem of the position of the zeros of theta functions. We then apply the developed general method to the inverse scattering problem.

Keywords

entire function Painlevé transcendent inverse scattering problem 

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Copyright information

© MAIK/Nauka 2008

Authors and Affiliations

  1. 1.Aliev Karachay-Cherkessia State UniversityKarachayevskRussia
  2. 2.Landau Institute for Theoretical PhysicsRASChernogolovka, Moscow OblastRussia

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